A function for the length in terms of the width is f(w) = 32 - w.
A graph of the function is shown in the image below.
A reasonable domain for the situation is 0 < w < 32.
In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);
P = 2(l + w)
Where:
- P is the perimeter of a rectangle.
- w is the width of a rectangle.
- l is the length of a rectangle.
By substituting the side lengths into the formula for the perimeter of a rectangle, we have the following;
P = 2(l + w)
64 = 2(l + w)
l + w = 32
l = 32 - w
Therefore, a function for the length in terms of the width is given by;
f(w) = 32 - w
In this context, we would use an online graphing tool to plot a graph of the function as shown in the image below.
Based on the function, we can logically deduce that the width of this rectangular play area cannot assume a negative value or zero, which implies that its width can neither be less than or equal to zero (0) nor greater than or equal to 32. Hence, a reasonable domain is all real numbers of w that satisfy this inequality 0 < w < 32.
Complete Question:
Katrina buys a 64-ft roll of fencing to make a rectangular play area for her dogs. Use 2(1 + w) = 64 to write a function for the length, given the width. Graph the function.
What is a reasonable domain for the situation?
Explain.